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GATE 2016 EC (EC2) – Question 60

Communications · Random Processes · 2 marks · Numerical answer

Let $X(t)=3V(t)-8$, where V is a zero-mean stationary process with autocorrelation $R_V(\tau)=4e^{-5|\tau|}$. The power in X is ________.

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Correct answer: 99 to 101

Explanation

Average power is the mean square. Expand $E[X^2]=9E[V^2]-48E[V]+64$.

The mean is zero and $E[V^2]=R_V(0)=4$. Consequently the total power is $9(4)+64=$ **100**. This includes the 64 units of power in the nonzero DC mean, not just the variance.

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